Activity Overview
In this activity, students use simulation to justify the concept of the Law of Large Numbers. They understand that as the sample size increases, the relative frequency of which an event occurs approaches the probability of that event happening. Students investigate the binomial and geometric probability functions, and determine the mean and standard deviation.

Before the Activity
Install the Statistics with List Editor application on the calculator using one of these two methods:

TI Connect™ , a TI Connectivity Cable, and the Unit-to-Unit Link Cable
TI-Navigator™ "send to class" feature
See the attached PDF file for detailed instructions for this activity
Print pages 95 - 108 from the attached PDF file for your class

During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Law of Large Numbers:

A player has a batting average of 0.333
Simulate the at-bat event as a toss of die and consider only 1, 2, or 3 spots
Find the cumulative success rate after 6 trials and 150 trials
Create a dotplot to view the data graphically
Note that as the sample size increases, the mean of the sample approaches the batting average of 0.333 (population mean)
Binomial Distribution:

Enter the number of trials, success probability, and the number of successful events
Determine the success rate of the event happening
Calculate the mean and the standard deviation for the binomial distribution
Set up a probability histogram and examine the center and spread
Simulate trials of the event and calculate the number of successes for each trial
Geometric Distribution:

Determine the probability of an event happening in a particular trial
Repeat the step for at least 50 trials
Enter the geometric distribution probabilities as a list
Determine the mean and set up a probability histogram
Simulate the first 10 trials and determine the trial in which the event first succeeded
Continue for 100 trials to obtain a better estimate

After the Activity
Review student results:

As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary